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any help in this would be deeply appreciated

i am new here

this is not homework. its an assignment?

this is my maths ia and i need help with it

i am asked to find a conjecture

see some of you might have heard about this question.

in an equilateral triangle ABC, a line segment is drawn from each vertex to a point on the opposite side so that the segment divides the side in the ratio 1:2, creating another equilateral triangle DEF

find a relationship between 1:n (like 1:2) and the area of the two triangles

i have done all the working out. i just need a conjecture and how to prove it